The 125 feet long line and the angles 65°10', and 60°10' obtained from the surveying equipment gives the length of the bridge as approximately 1234.2 feet.
<h3>Which rule can be used to find the length of the bridge?</h3>
Given;
Location of the tree = The other side of the river from the surveyor
Length of the line measured along the river, <em>L</em> = 125 feet
Angle to the tree from the start of the line = 65°10'
1° = 60'
10' = ((1/60)×10)° = (1/6)°
65°10' = (65 + 10/60)° = (65 + 1/6)°
Angle measured at the end of the line, <em>E</em> = 60°10'
Similarly;
E = 60°10' = (60 + 1/6)°
The interior angle, <em>S</em>, of the triangle formed by the tree and the line, at the start of the line is therefore;
Angle <em>S </em>= 180° - (65 + 1/6)° = (114+5/6)° (linear pair angles)
S = (114+5/6)°
From the angle sum property of a triangle, angle formed at the tree, <em>T</em>, is therefore;
T = 180° - ((114+5/6)° + (60 + 1/6)°) = 5°
According to the rule of sines, we have;
l/(sin T) = b/(sin E)
Where;
b = The length of the bridge
Which gives;
124/(sin 5°) = b/(sin (60 + 1/6)°)
b = (sin (60 + 1/6)°) × (124/(sin 5°)) ≈ 1234.2
- The length of the bridge, <em>b </em>≈ 1234.2 feet
Learn more about the rule of sines here:
brainly.com/question/4372174
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